step by step please. 30. Let p and q denote quaternions and let a,b E R....

Question

Question

30. Let p and q denote quaternions and let a,b E R. Show that (b) (ap + bq)apbq (c) N(q) = qq* = qq (d) pq)* = q*p* [Hint: Fi

step by step please.

Answer 1

Answer #1

The The Confua (ap าตั้ = a (fs-FiMj-ft).tb(%-971f.p Hence Hente leer e prove」 Hoace ponoved Hene pmivedl Ke po

Answer 2

Similar Homework Help Questions

1. The quaternions H are a set of "hyper-complex" numbers of the form p = a...

1. The quaternions H are a set of "hyper-complex" numbers of the form p = a + bi-cit dk. where a, b, c, d E R. Like the complex numbers, they can be added, conjugated by sending p ? p = a-bi-cj-dk, and the norm of a quaternion is given by lp-va2? 2 247. To multiply two quaternions, we use the algebra i2 = j2 = k2 =-1 ij=-ji = k jk=-kj = i ki=-ik = j a) Use the...
1. Let a, b E R with a < b and P { To,Ti,. . ....

1. Let a, b E R with a < b and P { To,Ti,. . . ,Tnf be a partition of the interval a, b] Denote ΔΧ,-2 j-rj-1 for J-1, 2, .. . , n. Consider a function f : [a,Ы-R. What do we need to require from f in order to be able to define the upper and lower Riemann sums of f over P?
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this E...

Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this Euclidean distance. (b) Find the plane that goes through O, P, Q. What is the intersection of this plane with the sphere? (Hint: use OP × OQ as the the normal vector) (c) Observe that the length of the arc PQ is 0 the angle between OP,0Q in radians. (Hint: You know how to find...

Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in Q[x] if...

Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in Q[x] if and only if the ideal (P, Q) of Z[x] generated by P and Q contains a non-zero integer (i.e. Z ∩ (P, Q) ̸= {0}). Here (P, Q) is the smallest ideal of Z[x] containing P and Q, (P, Q) := {αP + βQ|α, β ∈ Z[x]}. (iii) For which primes p and which integers n ≥ 1 is the polynomial xn − p...
1. (10 points) For the following questions, let p, q, r e Z be distinct positive...

1. (10 points) For the following questions, let p, q, r e Z be distinct positive prime integers, and define n=p?q?r. (a) How many distinct positive divisors does n = pq?r have? When counting positive divisors, do not count 1, but do count n itself (b) Using a result in the book, justify that n does not have any additional divisors beyond those given in (a).
1. Let a, b E R with a < b and P= {20, 21, ..., In}...

1. Let a, b E R with a < b and P= {20, 21, ..., In} be a partition of the interval [a, b]. Denote At; = x; – X;-1 for j = 1,2,...,n. Consider a function f : [a, b] → R. (a) (4 points) What do we need to require from f in order to be able to define the upper and lower Riemann sums of f over P? (b) (8 points) Define the upper and the lower...

5. Let P, Q, and R denote distinct propositional variables. Which of the following arguments are...

5. Let P, Q, and R denote distinct propositional variables. Which of the following arguments are valid? Justify your answer. (a) (P+Q), Q+ R), therefore (-PVR). (b) ((PAQ) + R), P, R, therefore Q.
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote...

. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w, r, and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p.
3. (RSA) Consider N-pq where p- 3 and q 5. (a) Calculate the value of N p. N 15 (b) Let c 3 be the encoding number....

3. (RSA) Consider N-pq where p- 3 and q 5. (a) Calculate the value of N p. N 15 (b) Let c 3 be the encoding number. Verify that c satisfies the require- ments of an encoding number (c) Find the decoding number d. [Hint: cd Imod(p 1)(q 1).] 3dI mod 2 (d) Consider the single character message 'b' (not including the quotes) Using its ASCII code it becomes the numerical plaintext message " 98 Calculate the encrypted message ba...

117. If R is any ring with identity, let J(R) denote the Jacobson radical of R. Show that if e is any idempotent of...

117. If R is any ring with identity, let J(R) denote the Jacobson radical of R. Show that if e is any idempotent of R, then J(e Re) eJ(R)e. 117. If R is any ring with identity, let J(R) denote the Jacobson radical of R. Show that if e is any idempotent of R, then J(e Re) eJ(R)e.